Martingale and Losing Streaks: The Math Behind the Bust
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In this guide (5)
Martingale means doubling your stake after every loss so that the first win recovers all losses plus one base unit. The math below shows why that works most of the time and fails badly when it fails. Model your own numbers in the Martingale bust calculator and the risk of ruin simulator. 18+ (or the higher legal age where you live), only where legal.
Example assumptions: every number below is our own calculation for an even-money bet that pays 2× with a win probability
p = 0.495(loss probabilityq = 0.505), which is what a 2× Dice bet at an assumed 1% house edge gives. Real games, edges and limits differ; check the game’s own rules.
How many losses a bankroll covers
With base stake b, the stake after n straight losses is b × 2ⁿ, and the total lost after k losses is:
L(k) = b(1 + 2 + … + 2^(k−1)) = b(2^k − 1)
Ignoring table limits and rounding, a bankroll B can fund at most k = floor(log₂(B/b + 1)) losses in a row. With 127 units you can cover 7 losses; the 8th would need 128 more.
Probability of a busting streak
A capped cycle ends at the first win or after k straight losses. With independent outcomes, the chance of hitting the loss cap is q^k. The table uses b = 1 and a cycle bankroll of exactly 2^k − 1 units:
| k (losses covered) | Bankroll needed (units) | Bust chance per cycle, q^k | EV per cycle (units) |
|---|---|---|---|
| 5 | 31 | 3.284% | −0.0510 |
| 6 | 63 | 1.659% | −0.0615 |
| 7 | 127 | 0.838% | −0.0721 |
| 8 | 255 | 0.423% | −0.0829 |
| 9 | 511 | 0.214% | −0.0937 |
| 10 | 1,023 | 0.108% | −0.1046 |
EV per cycle is (1 − q^k) × b − q^k × b(2^k − 1) = b[1 − (2q)^k]. It is negative for every k, and covering more losses (a larger k) makes the expected loss per cycle bigger, not smaller, because more money goes through the house edge. Extra bankroll only helps once it reaches the next 2^k − 1 threshold.
Streaks over a session
A bust is rare per cycle but likely over many bets. Using an exact run-length recursion for independent bets, the chance of seeing at least one run of k or more losses in N bets with q = 0.505:
| Bets (N) | Run of 7+ losses | Run of 10+ losses |
|---|---|---|
| 100 | 33.39% | 4.82% |
| 500 | 87.98% | 23.22% |
| 1,000 | 98.59% | 41.30% |
With a 127-unit bankroll that has not grown (k = 7), a run of 7 losses wipes it out. Each won cycle adds only one base unit, so cover grows slowly: in this model a run of 7+ losses appears in about 98.6% of 1,000-bet sequences. That exhausts a 127-unit cycle budget, but not necessarily a session bankroll that includes retained winnings; full ruin needs a model that tracks the balance, like the simulator above.
What Kelly says
The Kelly fraction for a bet with net odds d (1 for even money) is:
f* = (d × p − q) / d = p − q = 0.495 − 0.505 = −0.01
A negative Kelly fraction means the optimal stake is zero: no staking plan turns a negative-EV bet into a positive one. Systems change the shape of results and how much you wager in total, not the expected loss of about 1% per unit wagered in this model; more turnover means more total expected loss. The same applies to the Crash game and to auto-cashout strategies.
Safer habits if you play anyway
- Decide a session loss limit in money, not in “doublings”, and stop when you reach it.
- Use flat small stakes; they lose the same expected amount per unit wagered but avoid sudden large losses.
- Verify results with the provably fair verifier if you want to confirm rounds (background in our provably fair guide), but remember verification does not change the edge.
- Use the casino’s deposit and loss limits, or self-exclusion if play stops being fun.
Gambling can be addictive. Read our responsible gambling page. This page contains affiliate links: see the affiliate disclosure.
See what a staking level needs, with example numbers.
Frequently asked questions
Does Martingale beat the house edge?
No. Each bet keeps the same negative expected value, so any sequence of them does too. Martingale only reshapes outcomes into many small wins and rare large losses.
Where do the numbers on this page come from?
We calculated them ourselves from the formulas shown, using an example even-money bet with a 49.5% win chance (a 2× Dice payout at an assumed 1% edge). They are not measurements from any casino.
Does a table limit matter?
Yes. A maximum bet caps how many doublings you can make even with a large bankroll, which works like a smaller k in the formulas below. Check each game's limits.
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